Apparatus and methods for digital signal constellation transformation

ABSTRACT

Apparatus and method for digital signal constellation transformation are provided herein. In certain configurations, an integrated circuit includes an analog front-end that converts an analog signal vector representing an optical signal into a digital signal vector, and a digital signal processing circuit that processes the digital signal vector to recover data from the optical signal. The digital signal processing circuit generates signal data representing a signal constellation of the digital signal vector. The digital signal processing circuit includes an adaptive gain equalizer that compensates the signal data for distortion of the signal constellation arising from biasing errors of optical modulators used to transmit the optical signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority to U.S.application Ser. No. 16/022,573 filed Jun. 28, 2018, which is acontinuation of U.S. application Ser. No. 15/820,304 filed Nov. 21, 2017(now U.S. Pat. No. 10,038,505 issued Jul. 31, 2018), which is acontinuation of U.S. patent application Ser. No. 15/130,778, filed Apr.15, 2016 (now U.S. Pat. No. 9,853,734 issued Dec. 26, 2017), whichclaims priority to U.S. Provisional Patent Application No. 62/148,688,filed Apr. 16, 2015, incorporated herein by reference in their entiretyfor all purposes.

BACKGROUND Field

This disclosure relates to methods and systems for high-speed opticalcommunications.

Description of the Related Technology

There has been widespread adoption of personal electronic devicesincluding smart phones, tablets, notebooks, laptops, digital camera,video recorders, gaming systems, etc. These devices are being used tocommunicate ever-increasing quantities of data, such as betweendifferent personal electronic devices, between personal electronicdevices and peripheral devices (for example, display devices, externalstorage devices, etc.), and the like.

Enormous data communication demands are also present in a variety ofother contexts. For example, data centers are communicatingever-increasing amounts of data, and also require fast and reliable datacommunication between devices. The various methods and systems disclosedherein provide various improvements and benefits vis-à-vis existinghigh-speed communication technologies.

SUMMARY

An innovative aspect of the subject matter disclosed herein isimplemented in an integrated circuit comprising an analog front-endconfigured to convert an analog signal vector representing an opticalsignal into a digital signal vector; and a digital signal processingcircuit configured to generate signal data representing a signalconstellation of the digital signal vector. The digital signal vectorcomprises a digital representation of an in-phase (I) component and aquadrature-phase (Q) component of the optical signal. The digital signalprocessing circuit comprises an adaptive gain equalizer configured togenerate transformed signal data by compensating the signal data fordistortion of the signal constellation.

In various embodiments of the integrated circuit, the adaptive gainequalizer can be configured to generate an estimate of an angular tiltof the signal constellation and to compensate the signal data based onthe estimate of the angular tilt. The adaptive gain equalizer can beconfigured to generate the estimate of the angular tilt based on a sumof a plurality of cross-correlations of I and Q components of the signalconstellation. The sum of the plurality of cross-correlations can becomputed over a moving window of data samples obtained from the digitalsignal vector. The adaptive gain equalizer can be configured toiteratively revise the estimate of the angular tilt until I and Qcomponents of the transformed signal data are substantiallyuncorrelated. The adaptive gain equalizer can be configured toiteratively revise the estimate of the angular tilt based on a step gainthat changes based on a number of times the angular tilt has beenestimated. The adaptive gain equalizer can be configured to generate thetransformed signal data based on a transformation matrix that includesthe estimate of the angular tilt.

In various embodiments of the integrated circuit, the digital signalprocessing circuit can be configured to process the signal data for atleast one of feed forward equalization or carrier recovery prior tocompensating the signal data for distortion of the signal constellation.Various embodiments of the integrated circuit can further comprise adecision slicer configured to slice the transformed signal data. Thedistortion of the signal constellation can comprise at least one ofsqueezing, shifting, or tilting. In various embodiments, the opticalsignal can comprise a multi-level quadrature amplitude modulation (QAM)signal, a discrete multitoned (DMT) modulation signal, an orthogonalfrequency division multiplexing (OFDM), or a phase-shift keying (PSK)signal (including, but not limited to, a quadrature phase-shift keying(QPSK) signal).

Another innovative aspect of the subject matter disclosed herein isimplemented in a method of digital signal constellation transformationin an optical communication device. The method comprises receiving anoptical signal as an input to a coherent optical receiver; generating ananalog signal vector representing the optical signal using the coherentoptical receiver; converting the analog signal vector into a digitalsignal vector using an analog front-end; generating signal datarepresenting a signal constellation of the digital signal vector using adigital signal processing circuit; and compensating the signal data fordistortion of the signal constellation using an adaptive gain equalizerof the digital signal processing circuit. The digital signal vectorcomprises a digital representation of an in-phase (I) component and aquadrature-phase (Q) component of the optical signal.

In various embodiments of the method compensating the signal data fordistortion can comprise generating an estimate of an angular tilt of thesignal constellation and compensating the signal data based on theestimate of the angular tilt. The method can further comprisetransforming the signal data based on a transformation matrix thatincludes the estimate of the angular tilt. In various embodiments of themethod, generating the estimate of the angular tilt can comprise summinga plurality of cross-correlations of I and Q components of the signalconstellation. The method can further comprise iteratively revising theestimate of the angular tilt. Various embodiments of the method canfurther comprise processing the signal data for at least one of feedforward equalization or carrier recovery prior to compensating thesignal data for distortion of the signal constellation.

Yet another innovative aspect of the subject matter disclosed herein isimplemented in an integrated optical module comprising a coherentoptical receiver; and a transceiver. The coherent optical receiver isconfigured to receive an optical signal from an optical cable andgenerate an analog signal vector representing the optical signal. Thetransceiver is configured to process the analog signal vector togenerate a digital signal vector comprising a digital representation ofan in-phase (I) component and a quadrature-phase (Q) component of theoptical signal. The transceiver is further configured to generate signaldata representing a signal constellation of the digital signal vector.The transceiver comprises an adaptive gain equalizer configured togenerate transformed signal data by compensating the signal data fordistortion of the signal constellation.

In various embodiments of the integrated optical module, the adaptivegain equalizer can be configured to generate an estimate of an angulartilt of the signal constellation and to compensate the signal data basedon the estimate of the angular tilt. The adaptive gain equalizer can beconfigured to generate the estimate of the angular tilt based on a sumof a plurality of cross-correlations of I and Q components of the signalconstellation. The adaptive gain equalizer can be configured toiteratively revise the estimate of the angular tilt until I and Qcomponents of the transformed signal data are substantiallyuncorrelated. The adaptive gain equalizer can provide separatedistortion compensation for a first portion of the signal dataassociated with a horizontal polarization of the optical signal and fora second portion of the signal data associated with a verticalpolarization of the optical signal.

An innovative aspect of the subject matter disclosed herein isimplemented in an optical communication system comprising an opticaltransmitter configured to provide optical transmissions over an opticalnetwork; an optical receiver configured to receive an optical signalover the from the optical network and to generate an analog signalvector representing the optical signal; and a transceiver coupled to theoptical transmitter and to the optical receiver. The transceivercomprises an analog front-end; and a digital signal processing circuit.The analog front-end is configured to convert the analog signal vectorinto a digital signal vector, wherein the digital signal vectorcomprises a digital representation of an in-phase (I) component and aquadrature-phase (Q) component of the optical signal configured togenerate signal data representing a signal constellation of the digitalsignal vector. The digital signal processing circuit comprises anadaptive gain equalizer configured to generate transformed signal databy compensating the signal data for distortion of the signalconstellation.

In various embodiments of the optical communication system, the adaptivegain equalizer can be configured to generate an estimate of an angulartilt of the signal constellation and to compensate the signal data basedon the estimate of the angular tilt. The optical transmitter cancomprise one or more modulators and an automatic bias controllerconfigured to bias the one or more modulators.

BRIEF DESCRIPTION OF THE DRAWINGS

Example implementations disclosed herein are illustrated in theaccompanying schematic drawings, which are for illustrative purposesonly.

FIG. 1 is a schematic diagram of one embodiment of an opticaltransceiver module.

FIG. 2 is a schematic diagram of an optical transmitter that can beemployed to generate spectrally efficient optical signals.

FIG. 3A is a graph of two examples of constellation maps formed by thesymbols of a 16-level QAM signal.

FIGS. 3B and 3C are two examples of plots illustrating convergence oftilt angle as a function of the number of iterations for differentsignal-to-noise ratio (SNR) levels.

FIG. 4A is a schematic diagram of an optical transceiver systemincluding a transceiver chip according to one embodiment.

FIG. 4B is a schematic diagram of one embodiment of a transmit patharchitecture for the transceiver chip of FIG. 4A.

FIG. 4C is a schematic diagram of one embodiment of a receive patharchitecture for the transceiver chip of FIG. 4A.

FIG. 5 is a flowchart of a method of constellation transformationaccording to one embodiment.

FIG. 6 is a schematic diagram of a first optical communication system incommunication with another optical communication system via an opticalnetwork.

FIG. 7 is a plot of simulated bit-error-rate (BER) curves versus opticalsignal to noise ratio (OSNR).

FIG. 8 is a plot of one example of the measured average lane bit errorrate (BER) versus offset of a vertical phase bias voltage.

FIGS. 9A-9C show examples of constellation maps for vertical andhorizontal polarizations for different phase bias voltage offsets.

DETAILED DESCRIPTION OF EMBODIMENTS

The following detailed description is directed to certainimplementations for the purposes of describing the innovative aspects.However, the teachings herein can be applied in a multitude of differentways. As will be apparent from the following description, the innovativeaspects may be implemented in any high-speed communication system thatis configured to transmit and receive data between electronic deviceswhich can include laptops, notebooks, tablets, desk-top computers, datacenters, gaming devices, data storage systems, input/output peripheraldevices, display devices, etc. The innovative aspects may be implementedin or associated with data transport networks, storage area networks,enterprise networks, private networks, secure networks, financialnetworks, etc. Other uses are also possible.

A high-speed communication link can include an optical cable, such as afiber-optic cable. Additionally, an optical transmitter positioned onone end of the optical cable can transmit data to an optical receiverpositioned on the other end of the optical cable.

An optical transmitter can include optical modulators for transmittingoptical signals over the optical cable. In certain implementations, theoptical transmitter can employ automatic bias control to bias theoptical modulators to enhance the accuracy of transmissions. In oneexample, an optical transmitter includes a first optical modulator forgenerating in-phase (I) optical signal, a second optical modulator forgenerating a quadrature-phase (Q) optical signal, and an automatic biascontroller used to control biasing of the optical modulators. Forinstance, the automatic bias controller can generate a first biasvoltage that controls an offset of the first optical modulator, a secondbias voltage that controls an offset of the second optical modulator,and a third bias voltage that controls a phase difference between the Iand Q optical signals.

Although automatic bias control can enhance the performance ofcommunications over an optical cable, an automatic bias controller maynot precisely control the bias voltages to the desired values. Forexample, the bias voltages can include small perturbations associatedwith dithering and/or the voltage levels of the bias voltages can driftdue to a searching algorithm and/or a change in operating environment.

Errors in the optical transmitter's modulator bias voltages can lead todecoding errors at the optical receiver, such as burst errors and/orloss of frames. Sensitivity to errors in modulator biasing can beexacerbated in applications using high-order modulation formats, such as16-QAM or discrete multitoned (DMT) modulation.

Apparatus and method for digital signal constellation transformation areprovided herein. In certain configurations, an integrated circuitincludes an analog front-end that converts an analog signal vectorrepresenting an optical signal into a digital signal vector, and adigital signal processing circuit that processes the digital signalvector to recover data from the optical signal. The digital signalprocessing circuit generates signal data representing a signalconstellation of the digital signal vector. The digital signalprocessing circuit includes an adaptive gain equalizer that compensatesthe signal data for distortion of the signal constellation arising frombiasing errors of optical modulators used to transmit the opticalsignal.

The teachings herein can be used to increase the tolerance of an opticalreceiver to modulator biasing errors, including bias errors thatgenerate a phase error between I and Q components of the optical signal.For example, the optical receivers herein can exhibit enhancedrobustness to biasing errors arising from dithering and/or a searchingalgorithm of an optical transmitter's automatic bias controller.

In certain implementations, the adaptive gain equalizer compensates thesignal data for distortion based on detecting an amount of angular tiltof the signal constellation arising from modulator biasing errors. Inone example, a QAM signal constellation ideally has about a 90° aseparation between I and Q signal components, but modulator biasingerrors can lead to the QAM signal constellation being at a tilted anglewith respect to 90°. To compensate for the angular tilt, the adaptivegain equalizer can transform the signal data representing the signalconstellation using a transformation matrix that includes an estimatedvalue of the tilted angle.

In certain configurations, the estimated value of the titled angle isdetermined via iteration by adjusting a previous estimate of the titledangle based on a cross-correlation of I and Q components of thetransformed signal data. In certain implementations, the estimated valueof the titled angle is generated by iteratively adjusting the titledangle until the cross-correlation is within a convergence threshold. Thecross-correlation can be implemented in a variety of ways, and can beperformed over m data points of the signal constellation. In certainimplementations, the m data points are associated with a sum ofcross-correlations of a moving window of data samples. Thus, theestimated value of the titled angle can dynamically track changes to themodulator biasing errors. The iterative process can be controlled usinga step gain K that can be adjusted to control a trade-off betweenconvergence speed and stability. In certain implementations, the stepgain K can be dynamically controlled, such as by changing the step gainK based on a number of times the titled angle has been iterativelyestimated.

The integrated circuit can further include a decision slicer that slicesthe transformed signal data generated by the adaptive gain equalizer todetermine where particular data points of the signal constellationbelong. By compensating for distortion of the signal constellationbefore slicing, the bit error rate of an optical receiver can bereduced.

The teachings herein can be used to compensate for distortion of asignal constellation of a wide variety of formats, including, but notlimited to, quadrature amplitude modulation (QAM), discrete multitoned(DMT) modulation, orthogonal frequency division multiplexing (OFDM), andphase-shift keying (PSK) (including, but not limited to, quadraturephase-shift keying (QPSK)) for both coherent and direct-detectedsystems. Although example signal formats have been provided, a digitalsignal constellation transformation can be applied to other signals,such as signals having a signal constellation that is substantiallysymmetric with respect to an origin.

Examples of Optical Communication Devices

FIG. 1 is a schematic diagram of one embodiment of an opticaltransceiver module or integrated optical module 108. The opticaltransceiver module 108 includes a transceiver 110 and an optics block111. In the illustrated embodiment, the optics block 111 includes atransmit integrated tunable laser assembly (Tx iTLA) 112, a receiveintegrated tunable laser assembly (Rx iTLA) 118, an optical transmitter114, a driver 116, and a coherent receiver 120.

The optical transceiver module 108 receives transmit (Tx) data 124 froma host device on a host side, and processes the transmit data 124 togenerate a transmit optical signal 130 for transmission over an opticalcable on a line side. Additionally, the optical transceiver module 108receives a receive (Rx) optical signal 132 from the optical cable, andprocesses the receive optical signal 132 to generate receive data 126provided to the host device.

Although FIG. 1 illustrates one embodiment of an optical transceivermodule, an optical transceiver module can be implemented in a widevariety of ways. For example, the optical transceiver module 108 of FIG.1 can include more or fewer components and/or a different arrangement ofcomponents.

The optics block 111 can be implemented in a wide variety of ways. Inone example, the optics block 111 is implemented to communicate over anoptical cable based on Indium Phosphide (InP) modulator technology. Inanother example, the optics block 111 is implemented to communicate overan optical cable based on Lithium Niobate (LiNb) modulator technology.Although two examples of modulator technology have been provided, theteachings herein are applicable to a wide variety of modulatortechnologies.

In certain implementations, the transceiver 110 operates using aprogrammable host interface and/or programmable optical interfaceprotocol, thereby enhancing flexibility by providing compatibility witha wide variety of host devices and/or optical networks. In one example,the transceiver 110 includes a host interface that can communicate usingvarious standards such as, for example, 100 GE, OTU4, OTU3, and/or otherinterfacing standards. In another example, the transceiver 110 operatesin conjunction with the optics block 111 to transmit and receive opticalsignals associated with a wide variety of optical communicationprotocols, including for example, QAM, DMT, and/or PSK (including, butnot limited to, APSK and/or QPSK). The transceiver 110 can beimplemented with internal mapping and framing capability to providetranslation between the host interface protocol and the opticalinterface protocol. In certain implementations, the transceiver 110 hasat least one of a programmable data rate or programmable errorcorrection scheme.

The optical transceiver module 108 can communicate with a wide varietyof host devices, including, but not limited to, a mobile computingdevice, a personal computing device, a workstation, a peripheral device,a hub, and/or a network router. In certain implementations, the transmit(Tx) data 124 and/or the receive (Rx) data 126 are digital electricalsignals, such as multi-bit digital signals.

In the transmit direction of the optical transceiver module 108, thetransceiver 110 processes the transmit data 124 received from the hostside to generate an analog transmit signal vector 192. In one example,the analog transmit signal vector 192 includes four signals representingin-phase (I) and quadrature (Q) components for each of horizontal (H)and vertical (V) polarizations (represented as HI, HQ, VI, and VQ inFIG. 1). However, other implementations are possible.

In the receive direction of the optical transceiver module 108, thetransceiver 110 receives an analog receive signal vector 194 from thecoherent receiver 120 and performs signal processing functions that caninclude, for example, equalization and/or timing recovery to generatethe receive data 126. In one example, the analog receive signal vector194 includes four signals representing I and Q components for each ofhorizontal and vertical polarizations (represented as HI, HQ, VI, VQ inFIG. 1). However, other implementations are possible.

In the optics block 111, the Tx iTLA 112 generates an optical carriersignal and provides the optical carrier signal to the opticaltransmitter 114. The driver 116 operates in combination with the opticaltransmitter 114 to modulate the HI/HQ and VI/VQ signals onto opticalcarriers in horizontal and vertical polarizations, respectively, fortransmission over an optical cable on the line side. In the receivedirection, the Rx iTLA 118 generates a local oscillator (LO) signal atapproximately the carrier frequency of the received optical signal 132.The coherent receiver 120 receives the LO signal from the Rx iTLA 118and demodulates the incoming optical signal 132 to baseband to generatethe analog receive signal vector 194.

In one embodiment, the transceiver 110 generates an automatic gaincontrol (AGC) signal 188, which provides feedback to the coherentreceiver 120 based on the strength of the analog receive signal vector194. The AGC signal 188 may comprise a single signal or multiplesignals. In one example, the AGC signal 188 includes four gain controlsignals for controlling gain of HI, HQ, VI, and VQ signals of the analogreceive signal vector 194.

In certain implementations, the optical transceiver module 108 isimplemented as a pluggable module that can be integrated in an opticalcommunication system. Various features of the optical transceiver module108 of FIG. 1 can be similar to those described in commonly-owned U.S.Pat. No. 9,071,364, issued Jun. 30, 2015, and titled “COHERENT OPTICALTRANSCEIVER WITH PROGRAMMABLE APPLICATION MODES,” which is hereinincorporated by reference in its entirety for all purposes.

Although FIG. 1 illustrates one example of an optical communicationdevice that can be implemented to provide a constellation transformationalgorithm, the teachings herein are applicable to wide variety ofoptical communication devices. Moreover, although FIG. 1 illustrates aconfiguration including both a transmit path and a receive path, theteachings herein are also applicable to optical communication devicesthat omit a transmit path.

FIG. 2 is a schematic diagram of an optical transmitter 200 that can beemployed to generate spectrally efficient optical signals. The opticaltransmitter 200 includes an optical splitter 202 a, an optical coupler202 b, a horizontal I/Q optical modulating device 204, a vertical I/Qoptical modulating device 205, an automatic bias controller 206, ahorizontal photodetector 210 a, and a vertical photodetector 210 b.

Although FIG. 2 illustrates one embodiment of an optical transmitter, anoptical transmitter can be implemented in a wide variety of ways. Forexample, the optical transmitter 200 of FIG. 2 can include more or fewercomponents and/or a different arrangement of components.

The horizontal and vertical I/Q optical modulating devices 204 and 205can be used to convert electrical I/Q signals into optical signals withorthogonal optical polarizations (for example, horizontal (H) andvertical (V) polarizations). In the illustrated embodiment, thehorizontal and vertical I/Q optical modulating devices 204 and 205 eachinclude a phase shifter and a pair of Mach-Zehnder modulators to convertelectrical signals into I and Q optical signals or light waves. Forexample, the horizontal I/Q optical modulating device 204 includes afirst optical modulator 204 a, a second optical modulator 204 b, and aphase shifter 208 a. Additionally, the vertical I/Q optical modulatingdevice 205 includes a first optical modulator 205 a, a second opticalmodulator 205 b, and a phase shifter 208 b.

The optical transmitter 200 receives an input light beam along an inputpath 201 a, and generates a modulated optical signal along an outputpath 201 b. In one example, the input light beam corresponds to a lightoutput from the Tx iTLA 112 of FIG. 1, and the modulated optical signalcorresponds to the Tx optical signal 130 of FIG. 1. The input path 201 aand the output path 201 b can be implemented in a variety of ways, suchas by using an optical waveguide and/or an optical fiber.

The optical splitter 202 a splits the input light beam into a firstcomponent that is provided as an input to the horizontal I/Q opticalmodulating device 204 and a second component that is provided as aninput to the vertical I/Q optical modulating device 205. In theillustrated embodiment, the optical splitter 202 a includes apolarization beam splitter (PBS) that can split the input light beaminto a first component having horizontal (H) polarization (for example,TM polarization) and a second component having a vertical (V)polarization (for example, TE polarization). Although illustrated as apolarization beam splitter, the optical splitter 202 a can beimplemented in a wide variety of ways, such as by using waveguide and/orfiber-based optical components that split the optical power of the inputlight beam equally or unequally.

The first and the second components of the input light beam are coupledinto input optical waveguides 215 a and 217 a of the horizontal andvertical I/Q optical modulating devices 204 and 205, respectively. Anoptical splitter 203 a further divides the first component of the inputlight between the optical modulators 204 a and 204 b of the horizontalI/Q optical modulating device 204, and an optical splitter 203 c dividesthe second component of the input light between the optical modulators205 a and 205 b of the vertical I/Q optical modulating device 205.

Light inputted into optical modulators 204 a, 204 b, 205 a, and 205 b ismodulated with the electrical signals HI, HQ, VI and VQ, respectively.The light output of the optical modulators 204 b, 205 b is shifted usingthe phase shifters 208 a, 208 b, respectively. Additionally, the lightoutputs of the optical modulator 204 a and the phase shifter 208 a arecombined using the optical coupler 203 b and provided to an outputwaveguide 215 b. Furthermore, the light outputs of the optical modulator205 a and the phase shifter 208 b are combined using the optical coupler203 d and provided to an output waveguide 217 b.

The optical splitters 203 a and 203 c and the optical couplers 203 b and203 d can be implemented in a wide variety of ways, and can includedirectional couplers, multi-mode interference couplers and/or otheroptical components. As shown in FIG. 2, modulated light propagatingalong the output optical waveguides 215 b and 217 b is combined by anoptical coupler 202 b to generate the modulated optical signal on theoutput path 201 b. In the illustrated embodiment, the optical coupler202 b includes a polarization beam combiner. However, the opticalcoupler 202 b can be implemented in other ways, such as using opticalwaveguide and/or fiber-based components suitable for combining lightbeams.

The optical modulators 204 a, 204 b, 205 a and 205 b can be implementedin a wide variety of ways. In one example, the optical modulators 204 a,204 b, 205 a and 205 b are Mach-Zehnder modulators implemented on asubstrate including an electro-optic material such as, for example,lithium niobate (LiNbO₃) or indium phosphide (InP). For example, each ofthe Mach-Zehnder modulators can include an input waveguide that is splitinto a first branch and a second branch that extend along a length ofthe substrate and that are coupled together to form an output waveguide.

The illustrated optical transmitter 200 includes the automatic biascontroller 206, which generates bias voltages for biasing the horizontaland vertical I/Q optical modulating devices 204 and 205. For example,with respect to the horizontal I/Q optical modulating device 204, theautomatic bias controller 206 generates a first bias voltage (BIAS HI)for biasing the first optical modulator 204 a, a second bias voltage(BIAS HQ) for biasing the second optical modulator 204 b, and a thirdbias voltage (BIAS HPD) for biasing the phase shifter 208 a.Additionally, with respect to the vertical I/Q optical modulating device205, the automatic bias controller 206 generates a first bias voltage(BIAS VI) for biasing the first optical modulator 205 a, a second biasvoltage (BIAS VQ) for biasing the second optical modulator 205 b, and athird bias voltage (BIAS VPD) for biasing the phase shifter 208 b.

Although illustrated as part of the optical transmitter 200, in certainimplementations the automatic bias controller 206 is separate from theoptical transmitter 200. The automatic bias controller 206 can beimplemented in a wide variety of ways, and can include one or more dataconverters, amplifiers, detectors, filters, microprocessors,microcontrollers, digital signal processors (DSPs), field programmablegate arrays (FPGAs), memories, and/or other electronic circuitry.

The automatic bias controller 206 controls the bias voltages of thehorizontal I/Q optical modulating device 204 based on feedback receivedvia the horizontal photodetector 210 a. In one example, the automaticbias controller 206 controls a voltage level of the first bias voltage(BIAS HI) to control an offset of a horizontal I component of themodulated optical signal, controls a voltage level of the second biasvoltage (BIAS HQ) to control an offset of a horizontal Q component ofthe modulated optical signal, and controls a voltage level of the thirdbias voltage (BIAS HPD) to control a phase difference between thehorizontal I component and the horizontal Q component of the modulatedoptical signal to about 90 degrees. Similarly, the automatic biascontroller 206 controls the bias voltages of the vertical I/Q opticalmodulating device 205 based on feedback received via the verticalphotodetector 210 b.

The bias voltages or points of the horizontal and vertical I/Q opticalmodulating devices 204 and 205 can change due to a wide variety ofreasons, such as temperature changes, aging, and/or by dithering and/ora searching algorithm of the automatic bias controller 206. In theillustrated embodiment, the automatic bias controller 206 receivesfeedback via the horizontal and vertical photodetectors 210 a, 210 b.However, other implementations of feedback can be used.

In one embodiment, the automatic bias controller 206 applies a lowfrequency dither signal to one or more of the bias points of thehorizontal I/Q optical modulating device 204 and/or the vertical I/Qoptical modulating device 205. Additionally, the impact of the ditheringcan be observed via the horizontal and/or vertical photodetectors 210 aand 210 b. Thus, the automatic bias controller 206 can analyze and trackthe drifting of the biases by observing the impact of dithering.However, the automatic bias controller 206 can employ other trackingalgorithms.

Although FIG. 2 illustrates one example of an optical transmitter thatcan be used to transmit a modulated optical signal, a constellationtransformation algorithm can be applied to optical signals received froma wide variety of optical transmitters. For example, although FIG. 2illustrates a configuration in which the modulated optical signal is adual-polarization signal including both horizontal and verticalcomponents, a constellation transformation algorithm can be applied to areceived optical signal that includes a single polarization. Moreover,an optical receiver can provide a constellation transformation to anoptical signal that is received from an optical transmitter that doesnot employ automatic bias control.

Examples of Compensating for Drift in Modulator Bias Voltages

The growth in global data traffic can lead to congestions intelecommunication networks. Such networks can benefit from usingspectrally efficient modulation schemes including, for example,quadrature amplitude modulation (QAM) or discrete multitoned (DMT)modulation, which can accommodate more data channels within an availablebandwidth with little to no increase in interference between channels.

However, the complexity of higher-order modulation formats can result intighter margin and less tolerance to the impairment of opticaltransmission channels. For example, when operating near anerror-correction threshold, a small perturbation or drifting ofmodulator bias voltages can cause a series of burst errors or eventrigger loss of frames in the optical receiver. Sensitivity to biasvoltage drift can be exacerbated in implementations using complexmodulation formats, such as 16-QAM or DMT modulated signals.

An automatic bias controller, such as the automatic bias controller 206of FIG. 2, may efficiently compensate for drift of bias voltages used tocontrol I and Q offset (for example, BIAS HI, BIAS HQ, BIAS VI, and BIASVQ of FIG. 2). However, the automatic bias controller may not fullycompensate for the drift of the horizontal and/or vertical phase biasvoltages (for example, BIAS HPD and BIAS VPD of FIG. 2).

One reason for this can be that the strength of feedback associated withdrift of the horizontal and/or vertical phase bias voltage (for example,BIAS HPD and BIAS VPD of FIG. 2) can be significantly smaller, such asan order of magnitude smaller, than the strength of feedback associatedwith bias voltages used to control I and Q offset (for example, BIAS HI,BIAS HQ, BIAS VI, and BIAS VQ of FIG. 2). Accordingly, an automatic biascontroller may not accurately track drift of horizontal and/or verticalphase bias voltages, which can lead to bit-error rate (BER) fluctuationsand/or burst errors for signals with complex modulation formats.

In an optical communication system, data from the received opticalsignal can be recovered using a coherent receiver (for example, thecoherent receiver 120 of FIG. 1), which in turn can be processed by atransceiver (for example the transceiver 110 FIG. 1). The transceivercan perform one or more signal processing functions including, but notlimited to, chromatic dispersion correction, timing recovery, carrierrecovery, and/or feed-forward equalization (FFE) to compensate forsignal distortions arising from loss and/or noise in the opticalchannel.

In one example, a transceiver recovers data from an optical signal in a16-level quadrature amplitude modulated (QAM) format. In such anexample, the recovered symbols of the 16-level QAM signal can be mappedonto a constellation diagram or map that includes 16 symbols in atwo-dimensional X-Y plane scatter diagram. Additionally, each symbolrepresents 4-bits of digital data. Without any loss of generality, for a16-QAM modulated optical signal, the X-axis of the constellation map cancorrespond to the I component and the Y-axis can correspond to the Qcomponent of the recovered electrical signal, or vice versa.

However, errors in the optical transmitter's modulator bias voltages canlead to distortions in the constellation diagram, which can lead toerrors in recovering symbols. For example, the bias voltages can includesmall perturbations associated with dithering and/or the voltage levelsof the bias voltages can drift due to a searching algorithm and/or achange in operating environment.

Apparatus and method for digital signal constellation transformation areprovided herein. In certain configurations, an integrated circuitincludes an analog front-end that converts an analog signal vectorrepresenting an optical signal into a digital signal vector, and adigital signal processing circuit that processes the digital signalvector to recover data from the optical signal. The digital signalprocessing circuit generates signal data representing a signalconstellation of the digital signal vector. The digital signalprocessing circuit includes an adaptive gain equalizer that compensatesthe signal data for distortion of the signal constellation arising frombiasing errors of optical modulators used to transmit the opticalsignal.

In certain implementations, the adaptive gain equalizer compensates thesignal data for distortion based on detecting an amount of angular tiltof the signal constellation arising from modulator biasing errors. Inone example, a QAM signal constellation ideally has about a 90° aseparation between I and Q signal components, but modulator biasingerrors can lead to the QAM signal constellation being at a tilted anglewith respect to 90°. To compensate for an angular tilt, the adaptivegain equalizer can transform the signal data representing the signalconstellation using a transformation matrix that includes an estimatedvalue of the tilted angle.

In certain configurations, the estimated value of the titled angle isdetermined via iteration by adjusting a previous estimate of the titledangle based on a cross-correlation of I and Q components of thetransformed signal data. In certain implementations, the estimated valueof the titled angle is generated by iteratively adjusting the titledangle until the cross-correlation is within a convergence threshold. Thecross-correlation can be implemented in a variety of ways, and can beperformed over m data points of the signal constellation. In certainimplementations, the m data points are associated with a sum of thecross-correlation of a moving window of data samples. Thus, theestimated value of the titled angle can dynamically track changes to themodulator biasing errors. The iterative process can be controlled usinga step gain K that can be adjusted to control a trade-off betweenconvergence speed and stability. In certain implementations, the stepgain K can be dynamically controlled, such as by changing the step gainK based on a number of times the titled angle has been iterativelyestimated.

The integrated circuit can further include a decision slicer that slicesthe transformed signal data generated by the adaptive gain equalizer todetermine where particular data points of the signal constellationbelong. By compensating for distortion of the signal constellationbefore slicing, the bit error rate of an optical receiver can bereduced.

FIG. 3A is a graph of two examples of constellation maps formed by thesymbols of a 16-level QAM signal. The post-transformation constellationmap 305 formed by dashed circles (for example, 305 a, 305 b) representsthe location of the 16 symbols after application of one example of aconstellation transformation algorithm in accordance with the teachingsherein. Additionally, the pre-transformation constellation map 307formed by solid circles (for example, 307 a, 307 b) represents thelocation of the 16 symbols prior to application of the constellationtransformation algorithm.

As shown in FIG. 3A, the pre-transformation constellation map 307includes distortion associated with drift in horizontal and verticalphase bias voltages of horizontal and vertical I/Q optical modulatingdevices. Additionally, the post-transformation constellation map 305 hasbeen compensated to reduce the impact of distortion arising from driftin the horizontal and vertical phase bias voltages.

As shown in FIG. 3A, the 16 symbols of the post-transformationconstellation map 305 are arranged along four rows and four columns thatform a substantially rectangular grid parallel to the X- and Y-axes.However, the pre-transformation constellation map 307 illustrates thatdrift in the horizontal and/or vertical phase bias voltages can resultin a constellation map being shifted, squeezed and/or rotated withrespect to the X- and Y-axes.

For example, the pre-transformation constellation map 307 in FIG. 3A isoriented at an angle θ with respect to an axis parallel to the Y-axisand at an angle ψ with respect to an axis parallel to the X-axis. Invarious embodiments, the angle θ can be equal to the angle ψ. In someembodiments, the angle θ can be greater than or less than the angle ψ.Various algorithms can be used to compensate for any differences in themagnitude of angle θ and angle ψ. For example, carrier recoveryalgorithms employed by carrier recovery blocks in receiver systems(e.g., transceiver 110, transceiver chip 400, receiver path architecture450, optical receiver 608 a and 608 b) can align the constellation tothe diagonal axis centered at the origin such that the angle θ isapproximately equal to the angle ψ. Examples of carrier recoveryalgorithms employed to compensate for any differences in the magnitudeof angle θ and angle M can include coarse/fine carrier recovery,Viterbi-Viterbi estimation, etc.

In certain implementations, data recovered from an optical receivesignal is provided to a slicer to determine the received symbol. Forinstance, with respect to the example shown in FIG. 3A, a slicer can beused to determine which of the 16 symbols on the constellation diagramis closest to a received symbol, which may be degraded by noise, losses,and/or channel non-linearity. In additive white Gaussian noise (AWGN)channels, the slicer can determine the points by slicing about in themiddle. For example, for the constellation maps 305 and 307 illustratedin FIG. 3A, the decision boundary can be at [+0.5, 0, −0.5] for eachaxis. For instance, if a received symbol has an X-axis value less than−0.5 and a Y-axis value greater than +0.5, then the slicer may map thereceived symbol to symbol 305 a.

As discussed above, errors in modulator biasing can distort aconstellation. For example, drift of modulator phase bias voltages canresult in the constellation being shifted, squeezed and/or rotated. Forexample, a constellation can be rotated or squeezed into a diamondshape, as depicted by the pre-transformation constellation map 307 ofFIG. 3A. As described herein, an integrated circuit can include anadaptive gain equalizer that compensates data representing aconstellation map for errors in modulator bias voltages.

The distortion of the constellation map due to drift in horizontaland/or vertical bias voltages can result in a correlation between I andQ components of a constellation map. The distortion can lead to adecrease in extinction ratio or otherwise degrade performance

The pre-transformation constellation map 307 in FIG. 3A includesdistortion resulting from a drift of a horizontal phase bias voltage ofa horizontal I/Q optical modulating device 204 by an amount greater than5 degrees, in this example. As discussed above, due to signal processingfunctions such as, for example, feed-forward equalization (FFE) and finecarrier recovery (FCR) performed by a digital signal processing circuitof a transceiver, the pre-transformation constellation map 307 isaligned at about a 45 degree diagonal line and centered at about theorigin point such that the angle θ is approximately equal to the angleψ. For example, in various embodiments, the difference between angle θand the angle ψ can be less than 10%. The constellation distortion canbe viewed as a two-dimensional (2D) axis transformation

The teachings herein can be used to compensate for drift in horizontaland/or vertical phase bias voltages of optical modulating devices. Incertain configurations, a digital signal processing circuit processesreceived data using a constellation transformation algorithm (CTA).

In one embodiment, the constellation transformation algorithmcompensates for an angular tilt of a constellation map, such as thepre-transformation constellation map 307 of FIG. 3A, by applying atransformation matrix given by equation (1) below. By compensating theconstellation map for distortion before slicing, the bit error rate ofan optical receiver can be reduced.

$\begin{matrix}{\frac{1}{{\cos^{2}\theta} - {\sin^{2}\theta}}\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}} & (1)\end{matrix}$

In equation (1) above, θ represents the tilt of the constellation mapfrom an ideal position, such as an orthogonal position. In oneembodiment, θ is obtained iteratively using equation (2) below, where wiand wq are I and Q components, respectively, of a recovered opticalsignal after feed-forward equalization (FFE) and carrier recovery.

θ_(n)=θ_(n-1) +R(wi,wq)×K  (2)

In equation (2) above equation, K is the step gain factor, which can beadjusted to increase convergence speed and/or stability. The step gainfactor K can be selected based on the noise in the channel.Additionally, R(wi, wq) is the cross-correlation function of wi, wq. Inone embodiment. R(wi, wq) is given by equation (3) below, where m is thenumber of data points used in the cross-correlation function.

R(w _(i) ,w _(q))=Σ_(m) w _(i)[m]×w _(q)[m]  (3)

In one embodiment, at each n^(th) iteration, the integrated circuitimplementing the algorithm: (1) generates a new transformation matrixM_(n) based on the value of θ_(n) obtained in the n^(th) iteration inequation (1) above; (2) applies the new transformation matrix M_(n) tothe constellation map C_(n-1) obtained in the (n−1)^(th) iteration toobtain a new constellation map C_(n); (3) derives modified I and Qcomponents wi_(n) and wq_(n) from the new constellation map C_(n); and(4) determines the cross-correlation between the derived modified I andQ components wi_(n) and wq_(n).

In certain implementations, the algorithm is converged to the pointwhere R(wi_(n), wq_(n)) is close to zero(0), such as when R(wi_(n),wq_(n)) is less than a convergence threshold. For example, convergencecan be considered to be achieved if R(wi_(n), wq_(n)) is less than orequal to a threshold value (for example, less than or equal to 0.5, lessthan or equal to 0.1, less than or equal to 0.01, less than or equal to0.001, less than or equal to 0.0001 or values in between these rangesand sub-ranges). Converging the algorithm in this manner can be used todetermine when the I and Q signals are substantially uncorrelated. Inone embodiment, the algorithm is converged until the I and Q signals aresubstantially orthogonal. In certain implementations, the step gainfactor K can be adaptively controlled. For example, the step gain factorK can be adaptively changed over time such that it is relatively largein the beginning of the iterative process and is relatively small asR(wi_(n), wq_(n)) approaches zero(0).

In one embodiment, the integrated circuit implementing the algorithmprovides a constellation transformation separately to l/Q dataassociated with horizontal and vertical polarizations. Implementing theintegrated circuit in this manner enhances the accuracy of constellationtransformation by allowing different amounts of tilt adjustment to beprovided for a horizontal constellation map and for a verticalconstellation map. In such an embodiment, θ_(H) for adjusting ahorizontal constellation map is obtained by iteratively processing I andQ data associated with a horizontal polarization, and θ_(V) foradjusting a vertical constellation map is obtained by iterativelyprocessing I and Q data associated with a vertical polarization. In oneembodiment, the digital signal vector includes data representing asingle polarization modulation or a dual-polarization modulation, andthe integrated circuit is configurable between a first mode in which atilt adjustment is provided to the data representing the singlepolarization modulation, and a second mode in which a separate tiltadjustment for each polarization is provided to the data representingthe dual-polarization modulation. Thus, in one embodiment, an IC can beconfigurable to selectively process a signal of single polarizationmodulation or a signal of dual-polarization modulation. In anotherembodiment, an IC is operable to process signals of single polarizationmodulation but not of dual polarization modulation. In yet anotherembodiment, an IC is operable to process signals of dual-polarizationmodulation but not of single polarization modulation.

FIGS. 3B and 3C are two examples of plots illustrating convergence oftilt angle as a function of the number of iterations for differentsignal-to-noise ratio (SNR) levels. FIG. 3B illustrates convergence fora 30 dB SNR level, and FIG. 3C illustrates convergence for a 10 dB SNRlevel.

In the illustrated examples, SNR is calculated based on constellationsin an AWGN channel. Additionally, after the first 250 iterations, stepgain factor K is reduced by factor of 5 to improve stability. Becausethe data baud rate can be significantly higher than drifting associatedwith an automatic bias controller, the tracking algorithm can exhibitrobustness to variation in SNR. For example, when the SNR levelincreases, the number of data points m used in the cross-correlationfunction can be increased to average out the noise.

Example Transceiver Chip

FIG. 4A is a schematic diagram of an optical transceiver system 430according to one embodiment. The optical transceiver system 430 includesa transceiver chip or integrated circuit (IC) 400, a coherent opticalreceiver 404, an optical transmitter 422, a receive laser 414, and atransmit laser 418.

Although FIG. 4A illustrates one embodiment of an optical transceiversystem, an optical transceiver system can be implemented in a widevariety of ways. For example, the optical transceiver system 430 of FIG.4A can include more or fewer components and/or a different arrangementof components. Additionally, although illustrated in the context of anoptical transceiver system, a constellation transformation algorithm canbe employed in an optical communication system that omits a transmitpath.

As shown in FIG. 4A, the coherent optical receiver 404 generates ananalog receive signal vector 408 based on a received optical signal 406from an optical cable on a line side. The transceiver chip 400 processesthe analog receive signal vector 408 to generate receive data 403 for ahost device on a host side. As shown in FIG. 4A, the coherent opticalreceiver 404 receives a local oscillator signal from the receive laser414, which can be, for example, a continuous wave (CW) laser orintegrated tunable laser assembly. The transceiver chip 400 alsoprocesses transmit data 402 received form the host side to generate ananalog transmit signal vector 420 for the optical transmitter 422. Theoptical transmitter 422 modulates the analog transmit signal vector 420using an optical carrier signal from the transmit laser 418 to generatean optical transmit signal 424. Additional details can be similar tothose described earlier.

The illustrated transceiver chip 400 includes an analog front-end 410and a digital processing circuit 412 that includes an adaptive gainequalizer (AGE) 416. The transceiver chip 400 is implemented to providea constellation transformation algorithm to compensate for distortion ina constellation map recovered from the received optical signal 406.

In the illustrated embodiment, the analog front-end 410 receives theanalog receive signal vector 408, which includes HI, HQ, VI, VQ signalsin this example. Additionally, the analog front-end 410 processes theanalog receive signal vector 408 to generate a digital receive signalvector 409 that is provided to the digital processing circuit 412.

The digital signal processing circuit 412 can provide a wide variety ofprocessing to the digital receive signal vector 409, including, forexample, skew correction, filtering, clock recovery, decoding, I and Qamplitude imbalance correction, I and Q phase imbalance correction,compensation for phase noise of the optical carrier, chromaticdispersion compensation, and/or intersymbol interference (ISI)correction. The digital signal processing circuit 412 also generatesdata representing an original constellation map associated with I and Qsignal components recovered from the received optical signal 406.

The digital signal processing circuit 412 also includes the AGE 416,which implements a constellation transformation algorithm. The AGE 416can implement the constellation transformation algorithm on the datarepresenting the original constellation map, prior to decision slicingand demapping. As described earlier, the AGE 416 can perform across-correlation of I and Q components of the data representing theoriginal constellation map, and determine an initial estimate of thetilt angle of the original constellation map. When distortion of theoriginal constellation map is present, the AGE 416 can revise theestimate of the tilt angle θ of the original constellation map by aniterative process, as was described earlier. The AGE 416 can terminatethe iterative process once the cross-correlation between the I and Qcomponents is below a threshold value. The AGE 416 can further output atransformed constellation map that is compensated for tilt resultingfrom a drift in horizontal and/or vertical phase bias voltage. Incertain implementations, the AGE 416 applies a transformation matrixgiven in equation (1) above to the original constellation map.

Additional details of the optical transceiver system 430 of FIG. 4A canbe similar to those described earlier.

FIG. 4B is a schematic diagram of one embodiment of a transmit patharchitecture 440 for the transceiver chip 400 of FIG. 4A. The transmitpath architecture 440 receives data from a host device and processes thedata to generate an analog transmit signal vector for an opticaltransmitter.

The illustrated transmit path architecture 440 includes an egress hostinterface 4102, an egress framer/mapper 4104, a forward error correction(FEC) encoder 4106, a differential encoder and constellation mapper4108, a gear box 4109, a digital signal processing core 4110, aninterpolator 4112, a FIFO 4114, and a transmit analog front-end (AFE)4120. As shown in FIG. 4B, the differential encoder and constellationmapper 4108 includes a horizontal encoder and constellation mapper4108-a and a vertical encoder and constellation mapper 4108-b.Additionally, the digital signal processing core 4110 includes aspectral shaping and preemphasis filter 4111, and the transmit AFE 4120includes a skew compensation block 4122 and a digital-to-analogconverter (DAC) block 4126.

The egress host interface 4102 processes received data signals from ahost device. In certain implementations, the egress host interface 4102also includes a host demultiplexer configured to recover clock signalsfrom, and demultiplex, the received data signals. The egress hostinterface 4102 may also perform various processing functions such as,for example, equalization, signal integrity monitoring, and/or skewcompensation. The egress framer/mapper 4104 is configured to receivedata from the egress host interface 4102 and perform framing/mapping ofthe data according to a programmable framing/mapping protocol. The FECencoder 4106 can add error correction bytes according to a forward errorcorrection scheme suitable for a particular optical network. In thisexample, the differential encoder and constellation mapper 4108 receivesfour input signal data streams (for example, HI, HQ, VI, and VQ) andgenerates output signals using dual-polarization (DP) differential ornon-differential modulation formats, including, for example, PSK, BPSK,QPSK, 16QAM, and/or QAM of other indices or levels. In certainimplementations, processing is performed on a per-polarization basis(for example, separately for each of the horizontal and verticalpolarizations using encoders/mappers 4108-a and 4108-b, respectively),or using an encoding/mapping procedure that mixes polarizations.

The gear box 4109 can receive the signal stream from the differentialencoder and constellation mapper 4108 at a net data rate correspondingto a nominal data rate and reformat the data in the signal stream to anew data rate to accommodate any modifications to FEC code words.Additionally, the gear box 4109 generates an output signal streamincluding data at the nominal data rate (for example, at the same datarate as that of the input stream to the gear box 4109). Accordingly, thegear box 4109 is operable to change the parallelization factor of theegress path. In the illustrated embodiment, the digital signalprocessing core 4110 includes a spectral shaping and preemphasis filterfor each lane HI, HQ, VI and VQ. The spectral shaping and preemphasisfilter 4111 can be designed to have a frequency response thatpre-compensates for, or pre-equalizes, frequency-dependent attenuationof the electrical path between the DAC and the optical transmitter. Theinterpolator 4112 interpolates the data signal from the digital signalprocessing core 4110 to convert between sampling rates to enabledifferent components of the egress path architecture to operate atdifferent sampling rates.

The FIFO 4114 includes a data storage buffer that stores and queuesblocks of data received in parallel from the interpolator 4112. The FIFO4114 feeds the data to the transmit AFE 4120. The transmit AFE 4120includes the skew compensation filter 4122, which compensates the datafor skew introduced by the optical transmitter and the electrical signalpath associated with the signal lanes of the DAC block 4126. The DACblock 4126 receives the skew-compensated data, and generates analogsignals (HI, HQ, VI, VQ) for transmission to the optical transmitter.

The transmit path architecture 440 of FIG. 4B illustrates one example oftransmit path circuitry suitable for a transceiver chip. However, atransceiver chip can include transmit path architectures implemented ina wide variety of ways.

FIG. 4C is a schematic diagram of one embodiment of a receive patharchitecture 450 for the transceiver chip of FIG. 4A. The receive patharchitecture 450 receives an analog receive signal vector from anoptical receiver and processes the data to generate transmit data for ahost device.

The illustrated receive path architecture 450 includes a receive analogfront-end (AFE) 4148, a digital signal processing circuit 4155, adecision demapper or slicer 4176, a gear box 4177, an ingressframer/demapper 4178, a FEC decoder 4180, and an ingress host interface4182.

The illustrated receive AFE 4148 includes an analog-to-digital converter(ADC) block 4152 that converts the analog receive signal vector to adigital signal vector, which is processed by skew compensation filters4154 to compensate for differences in signal delays. The ADC block 4152can be programmable to operate with different resolutions and/ordifferent programmable data rates (for example, 32 GSa/s for DP-16QAM,64 GSa/s for DP-QPSK, at 128 Gb/s line rate). In certainimplementations, the receive AFE 4148 can include a line demultiplexerconfigured to parallelize the data for processing by the digital signalprocessing circuit 4155. In the illustrated embodiment, the receive AFE4148 also includes an automatic gain control circuit 4153 that detectsthe amplitude of the received analog signals and provides feedback tothe optical receiver to control gain.

The illustrated digital signal processing circuit 4155 includes ageneric matrix rotator 4156, a bulk chromatic dispersion (BCD) equalizer4158, a fiber length estimator 4160, a coarse carrier recovery block4162, a FIFO 4163, an interpolator 4164, a timing recovery block 4166, afeed-forward equalizer (FFE) 4170, a feedback fine carrier recoveryblock 4172, a feedforward fine carrier recovery block 4174, and an AGE416.

The generic matrix rotator 4156 applies a matrix transformation to thedigital signal vector to compensate for impairments associated withoptical demodulation in the optical receiver. Additionally, the BCDequalizer 4158 includes a horizontal compensator/equalizer 4158-a and avertical compensator/equalizer 4158-b, which operate to compensate forchromatic dispersion in the optical channel. Furthermore, the fiberlength estimator 4160 can estimate the extent or amount of chromaticdispersion introduced by the optical channel to select a mode ofoperation of the BCD equalizer 4158, and the coarse carrier recoveryblock 4162 performs an initial frequency acquisition or carrier recoveryof the received signal during a start-up phase.

The FIFO 4163 operates as a data storage buffer that stores and queuesblocks of data samples received from the BCD equalizer 4158. Theinterpolator 4164 processes data from the FIFO 4163 to correct for I/Qimbalances, such as skew between I and Q components and/or a differencein amplitude between I and Q components. The interpolator 4164 canperform sampling rate conversion to interface between the digital signalprocessing circuit 4155 and the receive AFE 4148 without loss of datasamples. The timing recovery block 4166 estimates the frequency andphase of the received data signal and generates timing information usedto recover the data. The FFE 4170 filters the data and appliesequalization to compensate for intersymbol interference (ISI) effectsimposed by the optical and electrical channels. The feedback finecarrier recovery block 4172 and the feedforward fine carrier recoveryblock 4174 further refine the carrier recovery performed by the coarsecarrier recovery block 4162. As shown in FIG. 4C, the feedback finecarrier recovery block 4172 provides a feedback signal FBK to thegeneric matrix rotator 4156.

The AGE 416 processes I and Q data from the feedforward fine recoverblock 4174. The AGE 416 provides a constellation transformationalgorithm, which can be as described earlier. In the illustratedembodiment, the AGE 416 provides constellation transformation to digitalI and Q data after feed-forward equalization (FFE) and carrier recovery.

In one embodiment, the AGE 416 provides a constellation transformationseparately to I/Q data associated with horizontal and verticalpolarizations. Implementing the AGE 416 in this manner enhances theaccuracy of constellation transformation by allowing different amountsof tilt adjustment to be provided for a horizontal constellation map andfor a vertical constellation map.

The decision demapper or slicer 4176 operates to decode transformedconstellation data from the AGE 416. The decision demapper or slicer4176 can provide a variety of information, such as the most probabledecoded bits based on the transformed constellation data. The gear box4177 can change a parallelization factor of the data from the decisiondemapper 4176. The ingress framer/demapper 4178 performs framing anddemapping of data so as to transform modulation symbols to source bits.The FEC decoder 4180 can be used to add error correction using a forwarderror correct scheme. The ingress host interface 4182 is used to providedata to a host device using a desired protocol. In certainimplementations, the ingress host interface 4182 includes a hostmultiplexer for multiplexing data provided to the host device.

The receive path architecture 450 of FIG. 4C illustrates one example ofreceive circuitry suitable for a transceiver chip. However, atransceiver chip can include receive path architectures implemented in awide variety of ways.

Example Method of Transforming Constellation Map to Compensate for Tilt

FIG. 5 is a flowchart of a method 500 of constellation transformationaccording to one embodiment.

The method 500 includes receiving an optical signal as depicted in block502. The optical signal can be similar to the received optical signal132 discussed above with reference to FIG. 1 and/or the received opticalsignal 406 discussed above with reference to FIG. 4A. The optical signalcan be received by a coherent receiver (for example, coherent receiver120 and/or coherent receiver 404).

As shown in block 504, I and Q components are recovered from thereceived optical signal. The I and Q components can recovered andprocessed as discussed above to compensate for various channel andoptical demodulator impairments. For example, the recovered I and Qcomponents can be obtained by converting the electrical signals receivedfrom the coherent optical receiver into digital format and processingthe digital signal using a digital signal processing circuit (forexample, the digital signal processing circuit 412), which can includethe one or more of various functional blocks described earlier. Incertain implementations, the I and Q components are processed for atleast one of feed-forward equalization (FFE) or carrier recovery.

An initial constellation map C_(initial) can be generated based on therecovered I and Q components as shown in block 506. Additionally, asshown in block 508, an initial angular tilt θ_(initial) of the initialconstellation map C_(initial) is estimated. In certain implementations,the tilt angle is measured with respect to an orthogonal constellationmap.

As shown in block 510, the tilt angle is iteratively adjusted based on across-correlation between I and Q components derived from intermediatetransformed constellation maps obtained during the iterative process.For example, the iterative process can be used to obtain a newtransformation matrix M_(n) obtained by substituting the value of θ_(n)obtained at each n^(th) iteration of the iterative process in equation(1) above. Additionally, the new transformation matrix M_(n) can beapplied to the constellation map C_(n-1) obtained in the (n−1)^(th)iteration of the iterative process to obtain a new constellation mapC_(n). Furthermore, modified I and Q components wi_(n) and wq_(n) can bederived from the new constellation map C_(n), and the cross-correlationbetween the derived I and Q components wi_(n) and wq_(n) can beprocessed to revise the estimate of the angular tilt.

The iterative process can be terminated when the cross-correlationbetween I and Q components derived from transformed constellation mapobtained during the n^(th) iteration of the iterative process R(wi_(n),wq_(n)) is about zero (0). For example, the iterative process can beterminated if R(wi_(n), wq_(n)) is less than or equal to a convergencethreshold value (for example, less than or equal to 0.5, less than orequal to 0.1, less than or equal to 0.01, less than or equal to 0.001,less than or equal to 0.0001 or values in between these ranges andsub-ranges). The tilt angle θ_(converged) obtained at the end of theiterative of the iterative process can be considered to be the convergedestimate of the tilt of the initial constellation map C_(initial)relative to the selected angular reference point.

At the end of the iterative process, a transformed constellation map isobtained as shown in block 514. The transformed constellation map can beequivalent to the constellation map obtained by applying atransformation matrix M calculated by substituting the tilt angleθ_(converged) to the initial constellation map C_(initial). Thetransformed constellation map is provided to the decision slicer, asshown in block 514, to decode the recovered I and the Q components forfurther processing. The method 500 can be implemented using anelectronic hardware processor such as for example the transceiver 110,the transceiver chip 400, the digital signal processing circuit 412, theoptical receivers 608 a and/or 608 b described herein.

In one embodiment, the method 500 of FIG. 5 is performed with respect toI/Q components obtained from an optical signal including a singlepolarization. In another embodiment, the method 500 is performed withrespect to two sets of I/Q components obtained from an optical signalincluding dual-polarization. For example, a first constellationtransformation can be performed on a first set of I/Q data associatedwith a horizontal polarization, and a second constellationtransformation can be performed on a second set of I/Q data associatedwith a vertical polarization. Thus, different amounts of tilt adjustmentcan be provided for a horizontal constellation map and for a verticalconstellation map. In such an embodiment, OH for adjusting a horizontalconstellation map is obtained by iteratively processing the first set ofI/Q data associated with horizontal polarization, and θ_(V) foradjusting a vertical constellation map is obtained by iterativelyprocessing I/Q data associated with a vertical polarization.

Additional details of the method 500 can be as described earlier.

Example Optical Communication Systems

FIG. 6 is a schematic diagram 600 of an optical communication system 604a in communication with another optical communication system 604 b viaan optical network 602.

The optical communication system 604 a includes an optical transmitter606 a, an optical receiver 608 a, and an AGE 610 a configured toimplement a constellation transformation algorithm to compensate for thetilt in a constellation map of a received signal as a result of biasdrifts. The optical communication system 604 b includes an opticaltransmitter 606 b, an optical receiver 608 b, and an AGE 610 bconfigured to implement a constellation transformation algorithm tocompensate for the tilt in a constellation map of a received signal as aresult of bias drifts.

The optical communication systems 604 a and 604 b can operate in arouter, a server, a hub, a datacenter system, a network backhaul system,a computer, a phone system, or any other system that transmits andreceives optical signals over the optical network 602. The opticalnetwork 602 can be a DWDM network, an OFDM network, a TDM network, etc.In various implementations, the optical communication systems 606 a and606 b can include one or more components and functional blocks similarto one or more of the components and functional blocks of thetransceiver architecture described above with reference to FIGS. 4A-4C.

Example Experimental Results

FIG. 7 is a plot of simulated bit-error-rate (BER) curves versus opticalsignal to noise ratio (OSNR) for optical signals generated by modulatorsin which one of the horizontal phase bias voltage or the vertical phasebias voltage had a drift of 2, 5 and 10-degrees. The BER curves areobtained by simulating constellations associated with a 16-levelQuadrature amplitude modulated (QAM) signal.

Curves 702, 704 and 706 represent the simulated BER curves when thehorizontal or the vertical phase bias voltage drift is 2, 5 and10-degrees respectively. It is noted that the power penalty at a BER of10⁻³ is about 2 dB for a 5-degree offset in bias. A 5-degree offset fora LiNbO₃ modulator translates to about 200 mV of fluctuation in the biasvoltage when biased around a null point of about 4V. Thus, smallfluctuations in the bias voltage can result in significant decrease inlink power budget. Curves 708, 710 and 712 represent the simulated BERcurves the constellation map is transformed by one implementation of aconstellation transformation algorithm to compensate for horizontal orthe vertical phase bias voltage offset of 2, 5 and 10-degreesrespectively. It is noted that the OSNR specification to obtain a BER of10⁻³ does not change when the constellation map is transformed tocompensate for the bias offsets.

To further test the robustness and effectiveness of the constellationtransformation algorithm, experiments were conducted with an integratedSystem-on-Chip (SoC) solution, which included analog front-ends (ADC andDAC), appropriate digital signal processing blocks, and signalgenerators and bit-error-rate testers. The setup and/or architecture ofthe SoC solution can be similar to the system and architecture depictedin FIG. 4A. For testing purposes a 253.27-Gb/s dual-polarization (DP)16-QAM optical signals were generated via Fujitsu DP-QPSK Mach-ZehnderModulator (MZM). Eight (8) channels with different pseudo random bitssequence (PRBS) were mapped onto the two 16-QAM constellations and sentthrough four on-chip DACs at 31.66-GBaud each. On the receiver side,four on-chip ADCs were used to sample the signals from an integratedcoherent receiver and eight (8) corresponding channel BER tester (BERT)was used to compute BER simultaneously after the digital signalprocessing blocks. The signals measured by the BERT were not compensatedfor the offsets in the bias voltage.

An on-chip diagnostic unit was used to capture the demodulatedconstellation after the digital signal processing block and input into acomputer for post processing which included transforming theconstellation map to compensate for the bias offset. Although the systemwas configured as dual-polarization system, an offset was introduced inonly the vertical phase bias voltage and BER was monitored. The BER ofoptical signals with horizontal-polarization were substantiallyunaffected since digital signal processing block could isolate the twopolarizations using constant modulus algorithm (CMA).

FIG. 8 is a plot of the measured average lane BER versus offset in thevertical phase bias voltage. The average lane BER can be obtained byaveraging the BER obtained for I and Q components. Curve 802 of FIG. 8illustrates the measured average lane BER obtained by post-processingthe de-modulated constellation using one implementation of aconstellation transformation algorithm (CTA) to compensate for theoffset in the vertical phase bias voltage and curve 804 obtained withouttransforming the constellation map to compensate for the offset in thevertical phase bias voltage. It is noted that the uncompensated BERcurve 804 shows an increase in BER as the offset in the vertical phasebias voltage increases indicating degradation of the quality of therecovered signals. It is also noted that the compensated BER curve 802shows relatively constant BER as the offset in the vertical phase biasvoltage increases indicating that the quality of the recovered signalsis maintained.

FIG. 9A illustrates the constellation maps for the vertical andhorizontal polarizations when the offset in the vertical phase biasvoltage was 0.1V. In FIG. 9A, constellation map 901 a depicts thein-phase (I) and quadrature-phase (Q) components recovered from theoptical signal with vertical polarization signal and constellation map901 b depicts I and Q components recovered from the optical signal withhorizontal polarization.

FIG. 9B illustrates the constellation maps for the vertical andhorizontal polarizations when the offset in the vertical phase biasvoltage is 0.3V. In FIG. 9B, constellation map 903 a depicts thein-phase (I) and quadrature-phase (Q) components recovered from theoptical signal with vertical polarization signal and constellation map903 b depicts the in-phase (I) and quadrature-phase (Q) componentsrecovered from the optical signal with horizontal polarization.

FIG. 9C illustrates the constellation maps for the vertical andhorizontal polarizations when the offset in the vertical phase biasvoltage was −0.5V. In FIG. 9C, constellation map 905 a depicts the I andQ components recovered from the optical signal with verticalpolarization signal and constellation map 905 b depicts the I and Qcomponents recovered from the optical signal with horizontalpolarization.

The constellation maps illustrated in FIGS. 9A, 9B and 9C depict theconstellation map prior to transformation to correct for the offset inthe vertical phase bias voltage. The post-processing constellationtransformation algorithm discussed herein can be used to compensate forthe tilt of the depicted maps with respect to orthogonal axes. Althoughthe constellation maps of FIGS. 9A, 9B and 9C illustrated variousexamples of constellations that can be compensated, the teachings hereincan be used to provide compensation to a wide variety of signalconstellations.

CONCLUSION

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense, as opposed to anexclusive or exhaustive sense; that is to say, in the sense of“including, but not limited to.” The word “coupled”, as generally usedherein, refers to two or more elements that may be either directlyconnected, or connected by way of one or more intermediate elements.Additionally, the word “connected”, as generally used herein, refers totwo or more elements that may be either directly connected, or connectedby way of one or more intermediate elements. Additionally, the words“herein,” “above,” “below,” and words of similar import, when used inthis application, shall refer to this application as a whole and not toany particular portions of this application. Where the context permits,words in the above Detailed Description using the singular or pluralnumber may also include the plural or singular number respectively. Theword “or” in reference to a list of two or more items, that word coversall of the following interpretations of the word: any of the items inthe list, all of the items in the list, and any combination of the itemsin the list.

Moreover, conditional language used herein, such as, among others,“can,” “could,” “might,” “can,” “e.g.,” “for example,” “such as” and thelike, unless specifically stated otherwise, or otherwise understoodwithin the context as used, is generally intended to convey that certainembodiments include, while other embodiments do not include, certainfeatures, elements and/or states. Thus, such conditional language is notgenerally intended to imply that features, elements and/or states are inany way required for one or more embodiments or that one or moreembodiments necessarily include logic for deciding, with or withoutauthor input or prompting, whether these features, elements and/orstates are included or are to be performed in any particular embodiment.

The above detailed description of embodiments of the invention is notintended to be exhaustive or to limit the invention to the precise formdisclosed above. While specific embodiments of, and examples for, theinvention are described above for illustrative purposes, variousequivalent modifications are possible within the scope of the invention,as those skilled in the relevant art will recognize. For example, whileprocesses or blocks are presented in a given order, alternativeembodiments may perform routines having steps, or employ systems havingblocks, in a different order, and some processes or blocks may bedeleted, moved, added, subdivided, combined, and/or modified. Each ofthese processes or blocks may be implemented in a variety of differentways. Also, while processes or blocks are at times shown as beingperformed in series, these processes or blocks may instead be performedin parallel, or may be performed at different times.

The teachings of the invention provided herein can be applied to othersystems, not necessarily the system described above. The elements andacts of the various embodiments described above can be combined toprovide further embodiments.

While certain embodiments of the inventions have been described, theseembodiments have been presented by way of example only, and are notintended to limit the scope of the disclosure. Indeed, the novel methodsand systems described herein may be embodied in a variety of otherforms; furthermore, various omissions, substitutions and changes in theform of the methods and systems described herein may be made withoutdeparting from the spirit of the disclosure. The accompanying claims andtheir equivalents are intended to cover such forms or modifications aswould fall within the scope and spirit of the disclosure.

What is claimed is:
 1. An integrated circuit device, the devicecomprising: a digital signal processing circuit configured to receive adigital signal vector and to generate signal data representing a signalconstellation of the digital signal vector; and wherein the digitalsignal processing circuit comprises an adaptive gain equalizerconfigured to generate an estimate of an angular tilt of the signalconstellation and to generate transformed signal data by compensatingthe signal data for distortion of the signal constellation based on theestimate of the angular tilt.
 2. The device of claim 1 wherein thedigital signal vector comprises a digital representation of an in-phase(I) component and a quadrature-phase (Q) component of the opticalsignal; and wherein the adaptive gain equalizer is configured togenerate the estimate of the angular tilt based on a sum of a pluralityof cross-correlations of I and Q components of the signal constellation.3. The device of claim 2 wherein the sum of the plurality ofcross-correlations is computed over a moving window of data samplesobtained from the digital signal vector.
 4. The device of claim 1wherein the digital signal vector comprises a digital representation ofan in-phase (I) component and a quadrature-phase (Q) component of theoptical signal; and wherein the adaptive gain equalizer is configured toiteratively revise the estimate of the angular tilt until I and Qcomponents of the transformed signal data are substantiallyuncorrelated.
 5. The device of claim 1 wherein the adaptive gainequalizer is configured to iteratively revise the estimate of theangular tilt based on a step gain, wherein the step gain changes basedon a number of times the angular tilt has been estimated.
 6. The deviceof claim 1 wherein the adaptive gain equalizer is configured to generatethe transformed signal data based on a transformation matrix thatincludes the estimate of the angular tilt.
 7. The device of claim 6wherein the transformation matrix is about equal to${\frac{1}{{\cos^{3}\theta} - {\sin^{3}\theta}}\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}},$ wherein θ is the estimate of the angular tilt
 8. Thedevice of claim 1 wherein the adaptive gain equalizer provides separatedistortion compensation for a first portion of the signal dataassociated with a horizontal polarization of the optical signal and fora second portion of the signal data associated with a verticalpolarization of the optical signal.
 9. The device of claim 1 furthercomprising a decision slicer configured to slice the transformed signaldata; and wherein the digital signal processing circuit is configured toprocess the signal data for at least one of feed forward equalization orcarrier recovery prior to compensating the signal data for distortion ofthe signal constellation; wherein the distortion of the signalconstellation comprises at least one of squeezing, shifting, or tilting;and wherein the digital signal vector comprises data representing asingle polarization modulation or a dual-polarization modulation. 10.The device of claim 1 wherein the optical signal comprises a multi-levelquadrature amplitude modulation (QAM) signal, a discrete multitoned(DMT) modulation signal, an orthogonal frequency division multiplexing(OFDM), or a phase-shift keying (PSK) signal.
 11. An integrated opticalmodule device, the device comprising: an optical receiver configured toreceive an optical signal from an optical cable and to generate ananalog signal vector representing the optical signal; and a transceiverconfigured to generate a digital signal vector from the analog signalvector, wherein the transceiver is further configured to generate signaldata representing a signal constellation of the digital signal vector,wherein the transceiver comprises an adaptive gain equalizer configuredto generate an estimate of an angular tilt of the signal constellationand to generate transformed signal data by compensating the signal datafor distortion of the signal constellation based on the estimate of theangular tilt.
 12. The device of claim 11 wherein the digital signalvector comprises a digital representation of an in-phase (I) componentand a quadrature-phase (Q) component of the optical signal; and whereinthe adaptive gain equalizer is configured to generate the estimate ofthe angular tilt based on a sum of a plurality of cross-correlations ofI and Q components of the signal constellation.
 13. The device of claim11 wherein the digital signal vector comprises a digital representationof an in-phase (I) component and a quadrature-phase (Q) component of theoptical signal; and wherein the adaptive gain equalizer is configured toiteratively revise the estimate of the angular tilt until I and Qcomponents of the transformed signal data are substantiallyuncorrelated.
 14. The device of claim 11 wherein the adaptive gainequalizer provides separate distortion compensation for a first portionof the signal data associated with a horizontal polarization of theoptical signal and for a second portion of the signal data associatedwith a vertical polarization of the optical signal.
 15. The device ofclaim 11 wherein the optical signal comprises a multi-level quadratureamplitude modulation (QAM) signal, a discrete multitoned (DMT)modulation signal, an orthogonal frequency division multiplexing (OFDM),or a phase-shift keying (PSK) signal.
 16. The device of claim 11 whereinthe digital signal vector comprises data representing a singlepolarization modulation or a dual-polarization modulation.
 17. Anoptical communication system, the system comprising: an opticaltransmitter configured to provide optical transmissions over an opticalnetwork; an optical receiver configured to receive an optical signalover the from the optical network and to generate an analog signalvector representing the optical signal; and a transceiver coupled to theoptical transmitter and to the optical receiver, the transceivercomprising: an analog front-end configured to convert the analog signalvector into a digital signal vector; and a digital signal processingcircuit configured to generate signal data representing a signalconstellation of the digital signal vector; wherein the digital signalprocessing circuit comprises an adaptive gain equalizer configured togenerate an estimate of an angular tilt of the signal constellation andto generate transformed signal data by compensating the signal data fordistortion of the signal constellation based on the estimate of theangular tilt.
 18. The system of claim 17 wherein the optical transmittercomprises one or more modulators and an automatic bias controllerconfigured to bias the one or more modulators.
 19. The system of claim17 wherein the optical signal comprises a multi-level quadratureamplitude modulation (QAM) signal, a discrete multitoned (DMT)modulation signal, an orthogonal frequency division multiplexing (OFDM),or a phase-shift keying (PSK) signal.
 20. The system of claim 17 whereinthe digital signal vector comprises data representing a singlepolarization modulation or a dual-polarization modulation.